From 9467b71e52ed75482b13b0305953d1a20dbdb416 Mon Sep 17 00:00:00 2001 From: wolf Date: Wed, 7 Apr 2004 00:13:26 +0000 Subject: [PATCH] Write text. git-svn-id: https://svn.dealii.org/trunk@8984 0785d39b-7218-0410-832d-ea1e28bc413d --- .../step-17.data/results.html | 136 ++++++++++++++++++ 1 file changed, 136 insertions(+) diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.html b/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.html index e67fccc1c1..220fdd537b 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.html +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.html @@ -1,2 +1,138 @@

Results

+ +

+If the program above is compiled and run on a single processor machine, it +should generate results that are very similar to those that we already got +with step-8. However, it becomes more interesting if we run it on a cluster of +computers. Most clusters have some kind of scheduling system, all of which +have different calling syntaxes - on my system, I have to use the command +bsub with a whole host of options to run a job in parallel - so +that the exact command line syntax varies. If you have found out how to run a +job on your system, you should get output like this for a job on 8 processors, +and with a few more refinement cycles than in the code above: +

+Cycle 0:
+   Number of active cells:       64
+   Number of degrees of freedom: 162 (by partition: 22+22+20+20+18+16+20+24)
+   Solver converged in 23 iterations.
+Cycle 1:
+   Number of active cells:       124
+   Number of degrees of freedom: 302 (by partition: 38+42+36+34+44+44+36+28)
+   Solver converged in 35 iterations.
+Cycle 2:
+   Number of active cells:       238
+   Number of degrees of freedom: 570 (by partition: 68+80+66+74+58+68+78+78)
+   Solver converged in 46 iterations.
+Cycle 3:
+   Number of active cells:       454
+   Number of degrees of freedom: 1046 (by partition: 120+134+124+130+154+138+122+124)
+   Solver converged in 55 iterations.
+Cycle 4:
+   Number of active cells:       868
+   Number of degrees of freedom: 1926 (by partition: 232+276+214+248+230+224+234+268)
+   Solver converged in 77 iterations.
+Cycle 5:
+   Number of active cells:       1654
+   Number of degrees of freedom: 3550 (by partition: 418+466+432+470+442+474+424+424)
+   Solver converged in 93 iterations.
+Cycle 6:
+   Number of active cells:       3136
+   Number of degrees of freedom: 6702 (by partition: 838+796+828+892+866+798+878+806)
+   Solver converged in 127 iterations.
+Cycle 7:
+   Number of active cells:       5962
+   Number of degrees of freedom: 12446 (by partition: 1586+1484+1652+1552+1556+1576+1560+1480)
+   Solver converged in 158 iterations.
+Cycle 8:
+   Number of active cells:       11320
+   Number of degrees of freedom: 23586 (by partition: 2988+2924+2890+2868+2864+3042+2932+3078)
+   Solver converged in 225 iterations.
+Cycle 9:
+   Number of active cells:       21424
+   Number of degrees of freedom: 43986 (by partition: 5470+5376+5642+5450+5630+5470+5416+5532)
+   Solver converged in 282 iterations.
+Cycle 10:
+   Number of active cells:       40696
+   Number of degrees of freedom: 83754 (by partition: 10660+10606+10364+10258+10354+10322+10586+10604)
+   Solver converged in 392 iterations.
+Cycle 11:
+   Number of active cells:       76978
+   Number of degrees of freedom: 156490 (by partition: 19516+20148+19390+19390+19336+19450+19730+19530)
+   Solver converged in 509 iterations.
+Cycle 12:
+   Number of active cells:       146206
+   Number of degrees of freedom: 297994 (by partition: 37462+37780+37000+37060+37232+37328+36860+37272)
+   Solver converged in 705 iterations.
+Cycle 13:
+   Number of active cells:       276184
+   Number of degrees of freedom: 558766 (by partition: 69206+69404+69882+71266+70348+69616+69796+69248)
+   Solver converged in 945 iterations.
+Cycle 14:
+   Number of active cells:       523000
+   Number of degrees of freedom: 1060258 (by partition: 132928+132296+131626+132172+132170+133588+132252+133226)
+   Solver converged in 1282 iterations.
+Cycle 15:
+   Number of active cells:       987394
+   Number of degrees of freedom: 1994226 (by partition: 253276+249068+247430+248402+248496+251380+248272+247902)
+   Solver converged in 1760 iterations.
+
+

+ +

+As can be seen, we can easily get to almost two million unknowns. In fact, the +code's runtime with 8 processes was less than 7 minutes up to (and including) +cycle 14, and 14 minutes including the last step. This, if the debug flag in +the Makefile was changed to "off", i.e. "optimized". Here is some output +generated in the 12th cycle of the program, i.e. with roughly 300,000 +unknowns: +

+ +

+ ux + uy +

+ +

+As one would hope for, the x- (left) and y-displacements (right) shown here +closely match what we already saw in step-8. What may be more interesting, +though, is to look at the mesh and partition at this step (to see the picture +in its original size, simply click on it): +

+ + +

+ grid + partition +

+ +

+Again, the mesh (left) shows the same refinement pattern as seen +previously. The right panel shows the partitioning of the domain across the 8 +processes, each indicated by a different color. The picture shows that the +subdomains are smaller where mesh cells are small, a fact that needs to be +expected given that the partitioning algorithm tries to equilibrate the number +of cells in each subdomain; this equilibration is also easily identified in +the output shown above, where the number of degrees per subdomain is roughly +the same. +

+ +

+It is worth noting that if we ran the same program with a different number of +processes, that we would likely get slightly different output: a different +mesh, different number of unknowns and iterations to convergence. The reason +for this is that while the matrix and right hand side are the same independent +of the number of processes used, the preconditioner is not: it performs an +ILU(0) on the chunk of the matrix of each processor separately. Thus, +it's effectiveness as a preconditioner diminishes as the number of processes +increases, which makes the number of iterations increase. Since a different +preconditioner leads to slight changes in the computed solution, this will +then lead to slightly different mesh cells tagged for refinement, and larger +differences in subsequent steps. The solution will always look very similar, +though. +

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